Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12573/395
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Conference Object Citation - Scopus: 1On the Existence of Positive Solutions for the Time-Scale Dynamic Equations on Infinite Intervals(Springer, 2020) Doǧan, Abdülkadir MuhittinThis paper investigates the existence of positive solutions to time-scale boundary value problems on infinite intervals. By applying the Leggett-Williams fixed point theorem in a cone, some new results for the existence of at least three positive solutions of boundary value problems are found. With infinite intervals, the theorem can be used to prove the existence of solutions of boundary value problems for nonlinear dynamic equations dependence on the delta derivative explicitly. Our results are new for the special cases of difference equations and differential equations as well as in the general time scale setting. © 2020 Elsevier B.V., All rights reserved.Article Citation - Scopus: 3Existence of Positive Solutions for P-Laplacian an M-Point Boundary Value Problem Involving the Derivative on Time Scales(Texas State Univ, 2014) Dogan, AbdulkadirWe are interested in the existence of positive solutions for the p-Laplacian dynamic equation on time scales (phi(P)(u(Delta)(t)))(V) a(t)f (t, u Delta(t), (t)) = 0, t is an element of (0,T)(T), subject to the multipoint boundary condition, u(0) = Sigma(m-2)(i=1) alpha iu, (xi(i)) = u Delta(T) = 0, where phi(p)(S) = vertical bar s vertical bar p(-2) s, p > 1, xi i is an element of [0, T](T,) 0 < xi 1 < xi 2 < . . . < xi m-2 < p(T). By using fixed point theorems, we prove the existence of at least three nonnegatvie solutions, two of them positive, to the above boundary value problem. The interesting point is the nonlinear term f is involved with the first order derivative explicitly. An example is given to illustrate the main result.Article Positive Solutions of Multipoint Φ-Laplacian BVPS With First-Order Derivative Dependence(World Scientific, 2023) Bachouche, Kamal; Tair, Hocine; Doǧan, Abdülkadir MuhittinThis paper concerns existence of positive solutions for a second-order boundary value problem of Sturm-Liouville type associated with a φ-Laplacian operator and posed on a bounded interval. Existence results are obtained by an adapted version of the Krasnosel'skii's fixed point theorem of cone expansion and compression. Some examples illustrate our results. © 2023 Elsevier B.V., All rights reserved.